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The following :
sage: %%cython
....: from sage.misc.prandom import random
....: cpdef complex crand(double x):
....: return x*random()+x*1j*random()
is about 77 times faster than its Python equivalent :
sage: def prand(x):
....: return CDF(2*(x*(random()-0.5)+I*x*(random()-0.5)))
sage: %timeit foo=crand(8)
The slowest run took 14.72 times longer than the fastest. This could
mean that an intermediate result is being cached.
1000000 loops, best of 3: 810 ns per loop
sage: 623000.0/810.0
769.135802469136
sage:
No small beer...
However :
sage: prand(8).parent()
Complex Double Field
sage: crand(8).parent()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-112-473e92fbb9eb> in <module>()
----> 1 crand(Integer(8)).parent()
AttributeError: 'complex' object has no attribute 'parent'
Is there a way to return a CDF (or RDF) value from a Cython function ?

1. Exactly the same way you would do it for a Python function: CDF(x)

2. If you want an even faster way, you need to use ComplexDoubleElement
internals: create the object with
ComplexDoubleElement.__new__(ComplexDoubleElement) and then manually set
the _complex attribute.

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